For New York City, it wasn't an unusual sight: a possibly mentally ill woman pacing and mumbling to herself on an elevated subway station platform.

The woman eventually took a seat on a bench Thursday night, witnesses later said. Then, without any warning or provocation, she sprang up and used both hands to shove a man into the path of an oncoming train.

As police sought to locate the unidentified woman Friday, Mayor Michael Bloomberg urged residents to keep the second fatal subway shove in the city this month in perspective. The news of the horrific death of a 46-year-old man from India came as the mayor touted drops in the city's annual homicide and shooting totals.

"It's a very tragic case, but what we want to focus on today is the overall safety in New York," Bloomberg said.

The New York Police Department released a sketch of the woman and surveillance video of her fleeing the area and interviewed witnesses, including some who described her as acting agitated before the attack.

Some witnesses said the man had been shielding himself from the cold by waiting in a stairwell before he ventured out onto the platform to see if the train was coming. They also said he had no interaction with the woman, who immediately darted down a stairway after she pushed him.

One witness told police that the man had no time to try to save himself. The witness turned away to avoid seeing the man getting crushed on the tracks.

Investigators identified the victim, who lived alone in Queens, through a smartphone and a prescription pill bottle he was carrying. They delayed releasing his name while they worked to notify his relatives in India.

Detectives were following leads from the public generated by the video and were checking homeless shelters and psychiatric units in a bid to identify the woman, described as Hispanic, heavyset, about 5 feet 5 and in her 20s. It was unclear whether the woman and the man knew each other.

The medical examiner said Friday that an autopsy found that the man died from head trauma.

Thursday night's killing came weeks after a man was pushed in front of a train in Times Square. A homeless man was charged with murder and is awaiting trial.